Can an unemployment claim be changed after the fact?

I was let go from my previous employer and filed for unemployment. I received notice that they refuted the claim, stating that I quit voluntarily.

I explained the situation to the UI rep during a phone call. A week later, I spoke with the representative again, who read me a rebuttal from my ex-employer - all of which was untrue or irrelevant. I answered their questions and stated my case again, sending the rep. documentation as proof.

I was ultimately awarded benefits; "discharged without misconduct on my part" being the reason in a nutshell.

My question is, if the employer appeals, are they held to their original claim that I quit voluntarily? Or, can they now change their position and try to prove misconduct on my part instead, in response to the UI representative's decision?